"The final frontier begins in this hall. Let's explore it together."
The Romulan Star Empire attempted to politically destabilize the region of space between the Alpha and Beta quadrants. This resulted in the Babel Crisis, which was resolved by the joint operation between Humans, Vulcans, Andorians and Tellarites. (ENT: "The Aenar") Starfleet Captain Jonathan Archer, commanding officer of Enterprise NX-01, started working to expose Romulan manipulation of interstellar events.
Initial talks for the formation of the Coalition took place on Earth in San Francisco and the participants included dignitaries from United Earth, Vulcan, the Andorian Empire, Rigel, Denobula, Coridan, and Tellar. (ENT: "Demons")
The initial conference was organized by United Earth Minister Nathan Samuels, who sought to build upon the work begun the previous year by Archer. The conference was disrupted when the terrorist organization Terra Prime threatened to destroy Starfleet Headquarters unless every non-Human left the Sol system within a day.
While Terra Prime was thwarted in this attempt, its creation of a Vulcan/Human hybrid prompted a great many outraged xenophobic protests among UE citizens that threatened to derail the creation of the Coalition, including demonstrations outside of the Vulcan Consulate and the Andorian Embassy.
Following the intervention of Archer and his crew as well as the death of Elizabeth, the cloned daughter of Charles Tucker III and T'Pol, however, the various dignitaries began to work in earnest to forge the alliance. (ENT: "Terra Prime")
The Coalition was the precursor to the United Federation of Planets, six years before its founding, and was made up of several worlds who later became integral to the formation and early history of the Federation. (ENT: "Zero Hour", "These Are the Voyages...")